Finite Group Databasebeta

← #25080454

Subgroups — #25080454

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145153C211yesmaximal, characteristic
2#19144724C211yesmaximal, characteristic, complemented
3#19144716C211yesmaximal, characteristic
4C8×Q8×D43C211yesmaximal, characteristic, complemented
5#19134054C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19134036C211yesmaximal, characteristic, complemented
8#19133976C211yesmaximal, characteristic, complemented
9#19133975C211yesmaximal, characteristic, complemented
10#19133942C211yesmaximal, characteristic, complemented
11#19133941C211yesmaximal, characteristic, complemented
12#19133357C211yesmaximal, characteristic, complemented
13#19133292C211yesmaximal, characteristic, complemented
14#19133287C211yesmaximal, characteristic
15C43×#1682C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583447C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583271C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583228—21no—
23#14583211—21no—
24#14583195C2211yescharacteristic
25#14583194C2211yescharacteristic
26#14583185C2211yescharacteristic
27#14583184C2211yescharacteristic
28#14583127—21no—
29#14583127—21no—
30#14583106C2211yescharacteristic
31#14583096C2211yescharacteristic
32#14583053—21no—
33#14583036—21no—
34Q8×C43⋊C8C2211yescharacteristic
35C8×Dic86—21no—
36C8×Dic86C2211yescharacteristic
37#14583023—21no—
38#14583023C2211yescharacteristic
39#14583006—21no—
40#14583003—21no—
41#14583000—21no—
42#14582996—21no—
43#14582990—21no—
44#14582990—21no—
45#14582955C2211yescharacteristic
46#14582955C2211yescharacteristic
47C4⋊C8×D43—21no—
48C4⋊C8×D43C2211yescharacteristic
49C4×C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43D411yescharacteristic
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—21no—
73C2×C8×D43—21no—
74C2×C8×D43D411yescharacteristic
75C2×C8×D43D411yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063316—21no—
79#13063312—21no—
80#13063305—21no—
81#13063301—21no—
82#13063296—21no—
83#13063296—21no—
84Q8×Dic43—21no—
85Q8×Dic43D411yescharacteristic
86C4×Dic86—21no—
87C4×Dic86C2311yescharacteristic
88#13063290—21no—
89#13063290—21no—
90#13063290D411yescharacteristic
91D4×Dic43—21no—
92D4×Dic43—21no—
93#13063283—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43D411yescharacteristic
96C42×D43—21no—
97C42×D43C2311yescharacteristic
98#13063259—21no—
99#13063258—21no—
100#13063257—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063249—21no—
118#13063246—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063235—21no—
122#13063235—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C2×Q16×C43—21no—
130C2×SD16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132#127×C43C2311yescharacteristic
133C4×Q8×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C2×D411yescharacteristic
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×C22⋊D43—41no—
150C22×Dic43—41no—
151Q8×D43—22no—
152Q8×D43—22no—
153#10621900—82no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43C2×D411yescharacteristic
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43#4111yescharacteristic
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86C2×D411yescharacteristic
163Q16×C43—42no—
164SD16×C43—42no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43C2×D411yescharacteristic
174C42×C43—21no—
175C42×C43C2411yescharacteristic
176C22⋊Dic43—41no—
177C22⋊Dic43—41no—
178#10621885—42no—
179#10621883—42no—
180#10621883—42no—
181#10621883—42no—
182(C2×D43)⋊C4—41no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—41no—
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—41no—
198C4×Dic43C2×D411yescharacteristic
199C4×Dic43C2×D411yescharacteristic
200C4×Dic43#4111yescharacteristic
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C8×D43—22no—
207C8×D43—41no—
208C8×D43—42no—
209C23×C43—41no—
210C22×D43#12111yescharacteristic
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43#13512yes—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—81no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—82no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—82no—
232C2×Dic43#12111yescharacteristic
233C2×Dic43#12111yescharacteristic
234C2×Dic43#12111yescharacteristic
235C4×D43—24no—
236C4×D43—22no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—21no—
241C4×D43—42no—
242Dic86—24no—
243Dic86—21no—
244Dic86—41no—
245Dic86—41no—
246Dic86—81no—
247Dic86#13512yes—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—41no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8#13712yes—
258#19263—431nomaximal, Sylow
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43C2×#12111yescharacteristic
263C2×D43—21no—
264C2×D43—21no—
265C2×D43#47112yes—
266C4×C43—22no—
267C4×C43—21no—
268C4×C43—41no—
269C4×C43—81no—
270C4×C43C2×#13511yescharacteristic
271C4×C43C2×#13511yescharacteristic
272C4×C43C2×#13711yescharacteristic
273C4×C43#57511yescharacteristic
274Dic43—21no—
275Dic43—21no—
276Dic43—22no—
277Dic43—21no—
278Dic43—41no—
279Dic43—81no—
280Dic43—81no—
281#3167—431no—
282#3113—431no—
283#3112—431no—
284C2×C8×Q8—431no—
285#1684—431no—
286#1684—431no—
287#1682—431no—
288#1682D4311yescharacteristic, complemented
289#1672—431no—
290#1672—431no—
291#1666—431no—
292#1666—431no—
293#1568—431no—
294#1552—431no—
295#1551—431no—
296C2×C43—161no—
297C2×C43#303711yescharacteristic
298C2×C43#305011yescharacteristic
299C2×C43C2×#47111yescharacteristic
300D43—22no—
301#533—431no—
302#532—431no—
303C2×C4×Q8—431no—
304#498—431no—
305#492—431no—
306#487—431no—
307#486C2×D4311yescharacteristic
308#483—861no—
309#480—861no—
310#477—431no—
311#477—431no—
312#475—431no—
313#475—431no—
314#465—861no—
315#465—861no—
316#462—431no—
317#462C2×D4311yescharacteristic
318#460—431no—
319#460C2×D4311yescharacteristic
320#451—861no—
321#448—861no—
322C8×Q8—431no—
323C8×Q8—431no—
324C8×Q8—431no—
325C8×Q8—861no—
326C8×Q8—861no—
327C8×Q8C2×D4311yescharacteristic
328#441—861no—
329#441—861no—
330#440—861no—
331#440—861no—
332C4×SD16—861no—
333C4×SD16—861no—
334#432—431no—
335#432—431no—
336C2×C4⋊C8—431no—
337C2×C4⋊C8—861no—
338C2×C4×C8—431no—
339C2×C4×C8—861no—
340#335—431no—
341#335C2×D4311yescharacteristic
342#334—431no—
343#334—431no—
344#333—431no—
345#333—431no—
346#332—431no—
347#332—431no—
348#332—431no—
349#332C2×D4311yescharacteristic
350#331—431no—
351#331C2×D4311yescharacteristic
352C43#1926311yescharacteristic, complemented, Sylow
353C2×#41—861no—
354C22×Q8—431no—
355C2×Q16—21no—
356C2×Q16—861no—
357C2×SD16—21no—
358C2×SD16—861no—
359C2×SD16—861no—
360C2×SD16—861no—
361C22×C8—431no—
362C22×C8—431no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8C22×D4311yescharacteristic
367#127C22×D4311yescharacteristic
368#125—861no—
369#124—861no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—861no—
373#121—861no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—431no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8C22×D4311yescharacteristic
382C4×D4—861no—
383C4×D4—861no—
384#117—861no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—861no—
387C2×C42—431no—
388C2×C42—861no—
389#107—861no—
390#107—861no—
391#106—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—21no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—861no—
418C22⋊C8—861no—
419C22⋊C8—861no—
420#97—861no—
421#97—861no—
422C4×C8—21no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8C22×D4311yescharacteristic
430#41—3442no—
431C2×Q8—21no—
432C2×Q8—431no—
433C2×Q8—861no—
434C2×Q8—862no—
435C2×Q8—862no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8D4×D4311yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—1721no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—1721no—
449Q16—42no—
450Q16—1722no—
451SD16—42no—
452SD16—1722no—
453SD16—1722no—
454SD16—1722no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—862no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—1721no—
465C2×C8—1722no—
466C2×C8D4×D4311yescharacteristic
467C2×C8D4×D4311yescharacteristic
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—431no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—1721no—
481C4⋊C4—1721no—
482C4⋊C4D4×D4311yescharacteristic
483C22⋊C4—1721no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C42—21no—
487C42—431no—
488C42—431no—
489C42—431no—
490C42—861no—
491C42—861no—
492C42—861no—
493C42—1721no—
494C42C23×D4311yescharacteristic
495C23—41no—
496C23—431no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—432no—
501Q8—864no—
502Q8—861no—
503Q8—3441no—
504Q8—1721no—
505Q8—1721no—
506Q8#1306334412yes—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—81no—
512D4—3442no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—431no—
517C2×C4—431no—
518C2×C4—431no—
519C2×C4—862no—
520C2×C4—864no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—3442no—
528C2×C4—1722no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4C2×D4×D4311yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4#41×D4311yescharacteristic
534C8—21no—
535C8—21no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—432no—
540C8—861no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—432no—
548C22—861no—
549C22—861no—
550C22#121×D4311yescharacteristic
551C4—21no—
552C4—22no—
553C4—41no—
554C4—81no—
555C4—861no—
556C4—861no—
557C4—861no—
558C4—862no—
559C4—3441no—
560C4—3441no—
561C4—1721no—
562C4#135×D4311yescharacteristic
563C4C2×#1306334411yescharacteristic
564C4#137×D4311yescharacteristic
565C4#1458369611yescharacteristic
566C2—161no—
567C2—862no—
568C2#1914406511yescharacteristic
569C2#1914417411yescharacteristic
570C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1682C2
socleC22×C43C2×#121
prime radical#14583447C22
hypercenter#1682D43
hypocenterC43#19263
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1682

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19144724C2semidirect
4. C8×Q8×D43C2semidirect
5. #19134054C2semidirect
6. #19134053C2semidirect
7. #19134036C2semidirect
8. #19133976C2semidirect
9. #19133975C2semidirect
10. #19133942C2semidirect
11. #19133941C2semidirect
12. #19133357C2semidirect
13. #19133292C2semidirect
15. C43×#1682C2semidirect
288. #1682D43semidirect
352. C43#19263semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191451532
#191447242
#191447162
C8×Q8×D432
#191340542
#191340532
#191340362
#191339762
#191339752
#191339422
#191339412
#191333572
#191332922
#191332872
C43×#16822
#1926343